Thats exactly the way I did it. PPL, JAA exams, ME, MEIR, then lastly the CPL which was on the multi. I ended up with the blue book on 200.2 hrs. I never quite understood why people took the CPL before the MEIR. I think it came from the integrated world but there is no need in the modular world. The only half valid argument I heard was that it is difficult to come from 55hrs Instrument flying back to 15 hrs VFR flying for the CPL.
It took a whole 10 minutes to get back into VFR flying, so its not a problem.